2025/11/24 by Ivan Hetman, Hetman, Ivan
Engineering · Mathematics · Computer Science · #graph theory and CDMA systems #Finite Group Theory Research #Coding theory and cryptography
paper · pdf · doi:10.48550/arxiv.2511.20708
Whereas Steiner systems S(2,k,v) with block length k ≤ 5 have large amount of examples and the existence is established for all admissible v, for k≥ 6 only few examples are known even for decided cases. In this paper the existence of S(2,9,369) is established and some new examples for other admissible pairs (k,v) are given. In particular, lots of new unitals of order 6 (or S(2,7,217)) together with S(2,7,175), S(2,7,259), S(2,8,120), S(2,8,504), S(2,9,513) are presented. Found examples suggest two conjectures on infinite series of designs.